Solving Two Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. For example, in the inequality 2x + 3 < 7, you would first subtract 3 from both sides and then divide by 2.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

1. Subtract 14 from both sides: -4x ≤ 40. 2. Divide by -4 (flip the sign): x ≥ -10.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

Solve the inequality 7n - 1 > 76.

Back

1. Add 1 to both sides: 7n > 77. 2. Divide by 7: n > 11.

Front

What is the solution to the inequality -3x - 4 < 5?

Back

1. Add 4 to both sides: -3x < 9. 2. Divide by -3 (flip the sign): x > -3.

Front

When do you not flip the inequality sign?

Back

You do not flip the inequality sign when you add or subtract a number from both sides.

Front

Solve for k in the inequality 7k - 2 ≥ -9.

Back

1. Add 2 to both sides: 7k ≥ -7. 2. Divide by 7: k ≥ -1.

Front

What is the first step in solving a two-step inequality?

Back

The first step is usually to isolate the term with the variable by adding or subtracting a constant from both sides.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality shows a number line with an open or closed circle at the boundary point and a shaded region indicating the solution set.

Front

What does the solution x ≤ 10 represent on a number line?

Back

It represents all numbers less than or equal to 10, including 10 itself, shaded to the left of 10.